Utopian Tree

 

The Utopian Tree goes through 2 cycles of growth every year. Each spring, it doubles in height. Each summer, its height increases by 1 meter.

A Utopian Tree sapling with a height of 1 meter is planted at the onset of spring. How tall will the tree be after  growth cycles?

For example, if the number of growth cycles is , the calculations are as follows:

Period  Height
0          1
1          2
2          3
3          6
4          7
5          14

Function Description

Complete the utopianTree function in the editor below.

utopianTree has the following parameter(s):

• int n: the number of growth cycles to simulate

Returns

• int: the height of the tree after the given number of cycles

Input Format

The first line contains an integer, , the number of test cases.
 subsequent lines each contain an integer, , the number of cycles for that test case.

Constraints

Sample Input

3
0
1
4

Sample Output

1
2
7

Explanation

There are 3 test cases.

In the first case (), the initial height () of the tree remains unchanged.

In the second case (), the tree doubles in height and is  meters tall after the spring cycle.

In the third case (), the tree doubles its height in spring (, ), then grows a meter in summer (, ), then doubles after the next spring (, ), and grows another meter after summer (, ). Thus, at the end of 4 cycles, its height is  meters.

Program:

#!/bin/python3

import math

import os

import random

import re

import sys

# Complete the utopianTree function below.

def utopianTree(n):

    i=0

    hgt=1

    while(i!=n):

        if i%2==0:

            hgt=hgt*2

        else:

            hgt+=1

        i+=1

    return hgt

if __name__ == '__main__':

    fptr = open(os.environ['OUTPUT_PATH'], 'w')

    t = int(input())

    for t_itr in range(t):

        n = int(input())

        result = utopianTree(n)

        fptr.write(str(result) + '\n')

    fptr.close()

Output:

Compiler Message

Success

Input (stdin)

• 2

• 0

• 1

Expected Output

• 1

• 2